The question of Ratzon Hashem is pretty spot on and it is quite profound however I think the answer cuts deep into our core.
We hold that aman and awoman are really two parts of one whole. We beleive that a marriage is not merely a partnership between one man and one woman.
It is the complete unification of man and woman.
As such the individual accomplishemnts of either of them are attributed to both of them.
This applies especially toa woman.
As in any company in order for success there must be defined roles. A well run company is one in which each person carrys out their role to perfection.
So to a Man and Woman create a family which is a “unit” charged with fulfilling Avodas Hashem. Hashem created each gender differently in order to ensure that biologicaly they are each suited to their roles.
The woman was given the role of being the “bacbone” the support while the man was given the role of action.
Interstingly in Jewish law the one who supports, the enabler is always given more reward then the actual doer and so to by women the Gemorah in Berachos (according to Rashi) states that they actually recieve more reward then men for enabling the learning of thier husbands.
Simchas Torah is not a celebration of Judaisim. It is a Siyum Hatorah. A siyum on the completion of the learnign of the Torah and the begining anew. When the men celebrate that is what hey are celebrating.
They are celebrating the completion of a year of them doing their Jobs.
A woman observing and watching Men celebrate what they have done, in essence watching the celebration of the completion of a task they have enabled.
Whjy would a woman want to be the one dancing and doing the actual completing of the Torah?
If one wants to do the “ratzon hashem then God has made his Ratzon clear by creating Men and Women differntly.
When women “switch” sides so they are the ones celebrating the Torah they are essentially declaring their desire to do that which God has said is not wanted.
It is not Ratzon hashem they are seeking to fulfill. It is Ratzonom that they are seeking to fulfill.
God wants women to be women not men,.